Data & spreadsheets · DCF Calculator
Gordon Growth Model Explained: Origins and Assumptions of Terminal Value
· Background
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The terminal value formula in most DCFs is the Gordon growth model, originally a way to value a stream of dividends. This post explains where it came from, how the formula is derived, and what it quietly assumes.
A formula memorised but never derived — why understanding the growing perpetuity changes how you set the growth rate
Memorising cash flow divided by r minus g hides the condition that makes the expression finite. The numerator is the first cash flow after the explicit horizon, and the denominator is the spread between discount and perpetual growth. Understanding those terms makes it harder to treat terminal growth as a harmless tuning input.
From recurring cash flows to a terminal model — how the growing perpetuity applies beyond its historical label
The implementation calls this Gordon Growth, but the repository does not provide historical sources establishing the outline’s dividend-model origin or named attribution. What it verifies is the broader use: a final forecast FCF is stepped forward once, then valued as a growing perpetuity representing all later cash flows.
Deriving the formula — summing an infinite geometric series to reach cash flow divided by (r − g)
A growing series starts with FCF at N plus one, then multiplies by one plus g each period while discounting by one plus r. Factoring the first term leaves a geometric series whose ratio is one plus g divided by one plus r. When that ratio is below one, summing the series yields FCF N plus one divided by r minus g.
The assumptions inside — constant growth forever, a stable discount rate, and growth strictly below that rate
The result assumes constant perpetual growth, a stable discount rate and growth strictly below that rate. ToolAcre validates the last condition and rejects equality or inversion, but it cannot establish that a company has reached a stable state. Mathematical validity is a minimum condition rather than evidence that the steady state exists.
Why it is used at the horizon — the practical need to stop forecasting and the trade-off of accepting a steady state
The formula appears at the horizon because detailed forecasting must stop somewhere. Replacing distant annual estimates with steady state reduces the number of explicit rows but concentrates value in fewer assumptions. A later horizon can reduce terminal share while requiring more unsupported year-by-year forecasts, so neither choice removes judgement.
Worked example — deriving a terminal value step by step from a final-year cash flow, then discounting it to today
Suppose hypothetical final-year FCF is 120, terminal growth is 2% and the discount rate is 9%. Next-year FCF is 122.4 and terminal value at year five is 1,748.57. Discounting that amount by 1.09 to the fifth power gives 1,136.45 today, before adding explicit forecast present values.
What this does not cover — alternative terminal methods and how to judge whether a business has reached steady state
Exit multiples, steady-state readiness and business-specific growth evidence are separate subjects. The tool supports an exit-multiple method, where terminal growth is ignored and the multiple applies to the final-year metric itself. Comparing methods can reveal dependence, but agreement does not prove either set of terminal assumptions is correct.
Know the formula's terms and conditions — how the ToolAcre DCF Calculator lets you test long-term growth assumptions against your own forecast
Read the terminal row as a contract with conditions: which cash flow begins the perpetuity, where the value is dated, what r and g are, and whether r exceeds g. ToolAcre exposes each component and rejects a broken denominator. It does not transform the formula into advice or a price.